What is the Greatest Common Factor of 7725 and 7732?

Greatest common factor (GCF) of 7725 and 7732 is 1.

GCF(7725,7732) = 1

We will now calculate the prime factors of 7725 and 7732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7725 and 7732.

How to find the GCF of 7725 and 7732?

We will first find the prime factorization of 7725 and 7732. After we will calculate the factors of 7725 and 7732 and find the biggest common factor number .

Step-1: Prime Factorization of 7725

Prime factors of 7725 are 3, 5, 103. Prime factorization of 7725 in exponential form is:

7725 = 3¹ × 5² × 103¹

Step-2: Prime Factorization of 7732

Prime factors of 7732 are 2, 1933. Prime factorization of 7732 in exponential form is:

7732 = 2² × 1933¹

Step-3: Factors of 7725

List of positive integer factors of 7725 that divides 7725 without a remainder.

1, 3, 5, 15, 25, 75, 103, 309, 515, 1545, 2575

Step-4: Factors of 7732

List of positive integer factors of 7732 that divides 7725 without a remainder.

1, 2, 4, 1933, 3866

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7725 and 7732. The biggest common factor number is the GCF number.
So the greatest common factor 7725 and 7732 is 1.

Also check out the Least Common Multiple of 7725 and 7732